The Kardar-Parisi-Zhang Equation and Universality Class (2013)

February 24-March 2, 2013

Organizers: Alexei Borodin, Jeremy Quastel, Herbert Spohn

The Kardar-Parisi-Zhang equation is a nonlinear stochastic partial differential equation widely used in the physics literature as a model of randomly growing interfaces, but until recently very poorly understood from the mathematical point of view. In one dimension, it is a member of a large universality class containing directed random polymers, stochastic Hamilton-Jacobi-Bellman equations, stochastically perturbed reaction-diffusion equations, stochastic Burgers equations and interacting particle models. The class is characterized by the unusual dynamic scaling exponent z=3/2. A number of breakthroughs about 10 years ago led to exact distributions of fluctuations for a few models, with conjectural extrapolation to the whole class. The distributions, surprisingly, turned out to be those recently discovered in random matrix theory. In the last few years there have been a second group of breakthroughs. Several models with adjustable asymmetry have recently been solved through which one can obtain, by scaling limits, exact distributions for various initial conditions for the KPZ equation itself. In addition, there have been breakthroughs in the well-posedness of the KPZ equation.

The goal of this workshop is to build on these advances in two directions. 1. Studying the integrability properties and statistics of the KPZ equation, as well as other models in the KPZ universality class. 2. Extending the universality of the KPZ equation. The new well-posedness theory should provide a route to proving scaling limits to the KPZ equation for a wider class of physical models.

Participants

Fedor Bogomolov, NYU/Courant

Mark Adler, Brandeis University

Gerard Ben Arous, NYU/Courant

Alexei Borodin, MIT

Pasquale Calabrese, Universita di Pisa

Reda Chhaibi, Universitat Zurich

Ivan Corwin, MIT/Microsoft Research

Percy Deift, NYU/Courant

Victor Dotsenko, University of Paris 6

Patrik Ferrari, University of Bonn

Alan Hammond, University of Oxford

Kurt Johnasson, KTH

Kostya Khanin, University of Toronto

Pierre Le Doussal, ENS, Paris

Pierre van Moerbeke, Université catholique de Louvain

Neil O’Connell, Warwick University

Jeremy Quastel, University of Toronto

Tomohiro Sasamoto, Chiba University

Timo Seppalainen, University of Wisconsin-Madison

Senya Shlosman, University of Marseilles

Herbert Spohn, Technische Universitat Munchen

Craig Tracy, UC Davis

Jon Warren, Warwick University